Table 1 Structural metrics of ERASMUS student network in 2013–2014 and subject based subnetworks (Abbreviations in rows: N - number of nodes, \(W_{tot}\) - the total number of weights/travels, L - the number of directed edges, E - the number of connections between HEIs not taking into account the direction and weight of edges, \(\gamma ^{in}\), \(\gamma ^{out}\) - the fitting parameter of power-law distribution in case of in-strengths, \(k_{sat}\) and \(k_{cut}\) represents the minimum and maximum node (in or out) strengths between the power-law distribution can be fit, i.e., log-log scale plotting of distribution the linear range is between the \(k_{sat}\) and \(k_{cut}\), G(N, L) - Erdős - Rényi random graph with the same number of nodes and edges as reference)

N

2,732

929

1715

1821

1273

1391

400

994

1001

\(W_{tot}\)

212,208

7,266

46,707

86,244

15,909

32,445

3,179

12,858

5,615

L

79,070

3,875

22,626

34,790

8,997

13,213

1,571

6,409

2,941

E

60,469

3,532

18,159

26,714

8,161

11,022

1,398

5,292

2,646

Average travels per edges

2.68

1.88

2.06

2.48

1.77

2.46

2.02

2.01

1.91

Rate of reciprocal edges

0.31

0.10

0.25

0.30

0.10

0.20

0.12

0.21

0.11

Density

0.028

0.008

0.016

0.026

0.010

0.017

0.020

0.013

0.006

Clustering coefficient

0.20

0.05

0.18

0.17

0.11

0.16

0.17

0.13

0.05

Clustering coefficient of G(N, L)

0.016

0.008

0.012

0.016

0.010

0.010

0.015

0.011

0.004

Number of components

7

14

5

4

9

5

9

8

13

\(\gamma ^{in}\)

-

3.11

3.26

3.87

3.33

2.19

2.48

3.30

2.49

\(k_{sat}^{in}\)

-

17

111

245

53

26

14

51

8

\(k_{cut}^{in}\)

-

83

513

712

171

535

127

179

51

\(\gamma ^{out}\)

-

3.7

3.88

4.16

3.52

2.55

2.78

3.28

2.39

\(k_{sat}^{out}\)

-

35

141

255

54

60

18

61

10

\(k_{cut}^{out}\)

-

96

445

680

181

989

80

228

79